Such cutting inserts, which if necessary have a peripheral land, are known in the art. In order to obtain a good surface quality when doing rough or finish machining, German 197 03 569 suggests providing a convexly shaped auxiliary cutting edge adjacent a planar free face. The cutting insert described in this publication can be made hexagonal seen from above on the cutting face, that is it has altogether six cutting edges of the same length and of which at least three are constituted as main cutting edges and three as auxiliary cutting edges. A concave chip-shaping groove extends on the cutting face parallel to the auxiliary cutting edges. Level with a perpendicular from the center of each main cutting edge and spaced from each main cutting edge there is preferably a raised chip-shaping element that is in particular formed as a nose-shaped projection of a central raised cutting-face plateau. This projection can have a three-corner planar top surface in the cutting-face plateau whose corners are pointed at the main cutting edges and of which side lines ending at these corners define angled flanks reaching to the cutting face, preferably at flank angles of 40° to 50°.